Sebelius is "considering entreaties from Democrats who want her to run" against Republican incumbent Pat Roberts, according to the report. Her candidacy would be polarizing, to say the least, given her tumultuous tenure at the Department of Health and Human Services, where she oversaw the disastrous rollout of the Affordable Care Act.

Brad Dayspring, a spokesman for the National Republican Senatorial Committee, had a one-word reaction to the news: "LOL."

Democrats have not held a Senate seat in Kansas since 1939 and President Barack Obama garnered only 38 percent of the vote there in the 2012 presidential election. Sebelius was popular as the state's two-term governor, however her time in the Obama administration has eroded her standing in the state.

A poll from the left-leaning Public Policy Polling in February found only 38 percent of Kansans viewed Sebelius favorably, compared with 55 percent who said they had an unfavorable view of her. According to the poll, "on the off chance" Sebelius would make a run for the seat, she would trail Roberts 52-38.

In general, Roberts is viewed as a vulnerable candidate. According to the PPP survey, his approval rating has plunged 12 points in the past year, in the wake of reports examining how little time he spends in Kansas. He is currently locked in a primary challenge with Milton Wolf, a former radiologist whose candidacy has already run into problems of its own.